Infinite horizon impulse control problem with continuous costs, numerical solutions

Stochastics ◽  
2017 ◽  
Vol 89 (6-7) ◽  
pp. 1039-1060
Author(s):  
Hani Abidi ◽  
Rim Amami ◽  
Monique Pontier
Keyword(s):  
Control Problem ◽  
Impulse Control ◽  
Numerical Solutions ◽  
Infinite Horizon ◽  
Impulse Control Problem

scholarly journals Infinite horizon impulse control problem with jumps and continuous switching costs

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Rim Amami ◽  
Monique Pontier ◽  
Hani Abidi
Keyword(s):  
Differential Equations ◽  
Control Problem ◽  
Stochastic Differential Equations ◽  
Optimal Strategy ◽  
Impulse Control ◽  
Backward Stochastic Differential Equation ◽  
Infinite Horizon ◽  
Backward Stochastic Differential Equations ◽  
Content Type ◽  
Impulse Control Problem

PurposeThe purpose of this paper is to show the existence results for adapted solutions of infinite horizon doubly reflected backward stochastic differential equations with jumps. These results are applied to get the existence of an optimal impulse control strategy for an infinite horizon impulse control problem.Design/methodology/approachThe main methods used to achieve the objectives of this paper are the properties of the Snell envelope which reduce the problem of impulse control to the existence of a pair of right continuous left limited processes. Some numerical results are provided to show the main results.FindingsIn this paper, the authors found the existence of a couple of processes via the notion of doubly reflected backward stochastic differential equation to prove the existence of an optimal strategy which maximizes the expected profit of a firm in an infinite horizon problem with jumps.Originality/valueIn this paper, the authors found new tools in stochastic analysis. They extend to the infinite horizon case the results of doubly reflected backward stochastic differential equations with jumps. Then the authors prove the existence of processes using Envelope Snell to find an optimal strategy of our control problem.

A Class of Stochastic Control Problem Governed by a Poisson Process

2012 ◽  
Vol 450-451 ◽  
pp. 46-55
Author(s):  
Shao Lin Tian ◽  
Ji Chun Li ◽  
Kun Hui Liu
Keyword(s):  
Optimal Control ◽  
Control Problem ◽  
Poisson Process ◽  
Objective Function ◽  
Impulse Control ◽  
Sufficient Condition ◽  
Signal Process ◽  
Impulse Control Problem ◽  
State Process ◽  
Optimal Impulse

In this paper, we examine an optimal impulse control problem of stochastic system, whose state follows a Brownian motion. Here we want to maximum the objective function. The main feature of our model is that the controlled state process includes an impulse control governed by a Poisson process. In other words, the set of possible intervention times are discrete, random and determined by the signal process. Here we not only present a theorem giving a sufficient condition on the existence of an optimal control and its corresponding objective function, but also provide an explicit solution obtained under some simplified conditions.

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